给定直径的毛虫树Steiner k-Wiener指数研究The Study of Steiner k-Wiener Index of Caterpillars with Given Diameter
孙旻昊,邢抱花,周鹏
摘要(Abstract)：
在化学图论中，分子拓扑指数对于刻画分子结构的特征与性质具有重要作用，可用于研究化合物的物理化学性质及生物活性等。其中，基于距离的拓扑指数的极值及其对应的极图是一类重要的研究课题。对于图G及其顶点子集S而言，Steiner距离d(S)定义为包含S的最小连通子图的边数，图G的Steiner k-Wiener指数SW_k(G)定义为所有k元顶点子集的Steiner距离之和。文章通过边扰动与作差法，研究了在给定直径的毛虫树中，具有最小、次小，以及最大、次大Steiner k-Wiener指数的极图问题。所得结论拓展了毛虫树类在该方向上的已有研究成果。作为一类重要的图不变量，Steiner k-Wiener指数从理论与应用两个层面扩展了经典Wiener指数的功能。
关键词(KeyWords)： 毛虫树;直径;Steiner距离;Steiner k-Wiener指数
基金项目(Foundation): 安徽省高等学校自然科学研究重点项目（KJ2021A0650）;; 安徽省研究生线下示范课程“图论”（2022xxsfkc038）
作者(Author): 孙旻昊,邢抱花,周鹏
DOI: 10.13757/j.cnki.cn34-1328/n.2025.03.003
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